Compactness and weak compactness of elementary operators on induced by composition operators on
Compactness conditions for elementary operators
Various topics concerning compact elementary operators on Banach algebras are studied: their ranges, their coefficients, and the structure of algebras having nontrivial compact elementary operators. In the first part of the paper we consider separately elementary operators of certain simple types. In the second part we obtain our main results which deal with general elementary operators.
Compactness of derivations from commutative Banach algebras
We consider the compactness of derivations from commutative Banach algebras into their dual modules. We show that if there are no compact derivations from a commutative Banach algebra, A, into its dual module, then there are no compact derivations from A into any symmetric A-bimodule; we also prove analogous results for weakly compact derivations and for bounded derivations of finite rank. We then characterise the compact derivations from the convolution algebra ℓ¹(ℤ₊) to its dual. Finally, we give...
Comparison of joint spectra for certain classes of commuting operators
Conditions for two self-adjoint operators to commute or to satisfy the Weyl relation.
Continuity of multilinear operators in weighted Herz spaces with extreme exponents.
Convergence of derivations on nearest algebras.
Corrigendum to “Commutators on ” (Studia Math. 206 (2011), 175-190)
We give a corrected proof of Theorem 2.10 in our paper “Commutators on ” [Studia Math. 206 (2011), 175-190] for the case 1 < q < p < ∞. The case when 1 = q < p < ∞ remains open. As a consequence, the Main Theorem and Corollary 2.17 in that paper are only valid for 1 < p,q < ∞.